A retired British businessman facing extradition to the US over allegations he plotted to export missile components to Iran will make an emergency application to the European court of human rights after being refused leave to appeal to the supreme court.

Christopher Tappin, from Orpington, in Kent, has said he was the victim of entrapment and that US customs agents enticed him into the deal, which he says made him a profit of $500 (£325). His is among a series of recent cases to focus attention on the UK-US extradition treaty, which critics allege is grossly biased in favour of America.

The 65-year-old's lawyers said they would apply to take the case to the supreme court, the country's highest legal body. But two high court judges, Lord Justice Hooper and Mr Justice Cranston, ruled that they would not permit the application, saying the case did not raise legal issues of sufficient general importance.

It means Tappin's lawyers have used all possible UK-based legal avenues to prevent his extradition.

His solicitor, Karen Todner, said an application would be lodged with the European court "in the next few days" seeking a halt on Tappin's extradition pending a full hearing of his case. Government solicitors had agreed not to remove Tappin for 14 days to allow for the application, Todner added.

Tappin admits arranging shipment of the batteries, a type used in US-made Hawk surface-to-air missiles, from the US to the Netherlands in 2006 but insists he had no idea about their final destination.

His lawyers told the appeal court that Tappin was set up by agents from the US Immigration and Customs Enforcement (ICE) agency who established a fake company, Mercury Global Enterprises, to "ensnare unsuspecting importers such as Mr Tappin".

The agents told Tappin they would obtain the export licences necessary for the batteries, the court was told. When Tappin raised concerns about this, one of the agents told him "this would not be a problem". The British businessman was sent paperwork by the agents saying that no licence was needed.

Tappin's argument was rejected by the high court. "Entrapment, as far as I can see, is simply unsustainable on the facts as alleged in the request," the appeal ruling said.

Tappin, who is the president of the Kent county golf union, has also unsuccessfully appealed against the extradition on human rights grounds, saying he is the primary carer for his wife, who has a rare and debilitating auto-immune condition, Churg-Strauss syndrome.

The most prominent case to focus attention on the 2003 extradition treaty between Britain and the US is that of Gary McKinnon, whom US prosecutors have sought since 2005 for hacking into top-secret US military computers.

McKinnon, 45, admits the hacking but says he was looking for evidence of UFOs. His supporters argue that McKinnon, who has Asperger's syndrome, is extremely vulnerable and that any trial should take place in Britain.

A more recent case is that of Richard O'Dwyer, a 23-year-old student from Chesterfield. This month a magistrates court approved his extradition to the US for running a website posting links to pirated TV shows and films, despite significant doubts over whether such sites break any UK laws. O'Dwyer has never visited the US and his website used servers based in other countries.